Reduced complexity signal converter

ABSTRACT

In a signal converter which derives from an input signal having a sample rate R/q an output signal having a larger sample rate R, the input signal is combined with a feedback signal in a subtracter to form a single combined signal. Samples of the combined signal are mapped into a larger number of output samples by a mapper forming part of a mapping arrangement which also produces the feedback signal. The formation of a single combined signal makes the signal converter less complex in design than it would be if a number of combined signals were formed. In a further embodiment a noise shaping filter is interposed between the subtracter and the mapper.

BACKGROUND OF THE INVENTION

The invention is related to a signal converter for converting an inputsignal into an output signal, the signal converter including a combinerfor deriving a combined signal from the input signal and a feedbacksignal and mapping arrangement configured for deriving from the combinedsignal both a plurality of samples of the output signal and the feedbacksignal.

Such a signal converter is known from U.S. Pat. No. 5,272,655.

Signal converters of this type are used, for example, indigital-to-analog converters operating according to the bit streamprinciple. In such converters, an input signal having a first samplefrequency is transformed in an output signal having a second samplefrequency. The input signal has a spectrum which is periodic with aperiod corresponding to the first sample frequency. Once the sample ratehas been increased, the frequency spectrum of the output signal havingthe second sample rate continues to be periodic with a periodcorresponding to the first sample rate. However, a signal is desiredwhich has a frequency spectrum that is only periodic with a periodcorresponding to the second (higher) sample rate. In order to realizethis, a filter is required which eliminates the undesired frequencycomponents. In a bitstream type converter, this filtering is performedby a low pass filter present in the feed forward path of the bitstreamtype converter.

A problem with bit stream type converters, especially with high ratiosof the second and first sample frequency is the high operating frequencyof the sample rate converter. In the signal converter according to theabove mentioned U.S. patent, the operating frequency is reduced with afactor p. This is obtained by using a mapping arrangement whichgenerates in response to one sample of the output signal of thecombining means p samples of the output signal. The output samples aredownsampled using a plurality of feedback filters. The feedback signalsare combined with filtered input signals to obtain a plurality ofdifference signals. Each of these difference signals are filtered usinga separate filter and finally combined into the combined signal. Thenumber of filters is equal to the order of the filtering required, whichcan result in an increased complexity. This increased complexity leadsto a larger amount of silicon area if the signal converter is realizedin hardware.

OBJECT AND SUMMARY OF THE INVENTION

The object of the present invention is to provide a signal converteraccording to the preamble of which the complexity has been reduced.

Therefore the signal converter according to the present invention ischaracterized in that the combiner is arranged for deriving one singlecombined signal, and in that the mapping arrangement is configured forderiving the feedback signal representing a decimated or downsampled andanti alias filtered output signal.

The invention is based on the recognition that it is possible to replacethe plurality of filters by one single filter which performsdownsampling and anti aliasing filtering of the output signal in orderto obtain the feedback signal.

An embodiment of the invention is characterised in that the combinercomprises a noise shaping filter for obtaining the combined signal.

By introducing a noise shaping filter for filtering the combined signal,it becomes possible to optimize both the noise shaping characteristicsof the signal converter and the anti-aliasing filtering performed in thefeedback path.

A further embodiment of the invention is characterized in that themapping arrangement is configured for providing a further signalrepresenting the downsampled output signal, and in that the noiseshaping filter also is arranged for deriving a filtered further signalfor obtaining the combined signal.

The introduction of a further downsampled signal into the noise shapingfilter, results in additional degrees of freedom, which can be exploitedfor optimizing the sample rate according to the present invention. Inparticular it allows a substantial independent optimization of theanti-aliasing filtering and the noise shaping characteristics.

A further embodiment of the invention is characterized in that thedecimating and anti alias filtering has filtering has an impulseresponse corresponding at least partly to the impulse response of a combfilter.

It has turned out that a comb filter is very suitable to perform thefiltering operation in the feedback path. Its complexity is very low,and it can attain good suppression of aliasing components. It also has asubstantially constant transfer function in the pass band.

A further embodiment of the invention is characterized in that themapping arrangement is configured for recursively determining thesamples of the output signal from a filtered error signal, the errorsignal being representative of the difference between the input sampleand a weighted sum of output samples already determined.

By recursively determining the samples of the output signal from thefiltered difference between an input sample and a weighted sum of outputsamples already determined, it is possible to suppress undesired signalsin the output signal by choosing a proper transfer function of thefilter used for the filter operation.

A further embodiment of the present invention is characterized in thatthe mapping arrangement is configured for filtering the error signalaccording to a high-pass transfer function.

By using a high pass filtering function, it is possible to suppressundesired signals in the frequency band covering the input signal. Knownsignal converters often suffer from spurious signals in the frequencyrange of the input signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be explained with reference to the drawings,which shows in:

FIG. 1, a signal converter, being here a sample rate converter accordingto the present invention;

FIG. 2, a sample rate converter according to the invention in which anoise shaping filter is used;

FIG. 3, a sample rate converter according to the invention using asecond order noise shaping filter;

FIG. 4, a sample rate converter according to the present invention usinga third order noise shaping filter;

FIG. 5, a mapper to be used with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In the sample rate converter according to FIG. 1, an input signal Y(Z)having a sample rate R/q is applied to a first input of a combiner,being here a subtracter l. The output signal of the subtracter 1 isconnected to an input of mapping means 2. In the mapping arrangement 2,the output signal of the subtracter 1 is connected to a mapper 3. Theoutput of the mapper 3 is connected to an input of weighted summingmeans 4 and to an input of a parallel to series converter 5. The outputof the weighted summing means 4 with output signal X_(f2) (Z) isconnected to a second input of the subtracter 1. The output of theparallel to series converter 5, carrying output signal X(z) constitutesthe output of the sample rate converter.

In the sample rate converter according to FIG. 1, the input signal Y(Z),the feedback signal x_(f2) (Z) and the signal B(Z) have a sample rateR/q, in which R is the sample rate of the output signal X(z). The mapper3 provides q output samples per input sample B(Z). It is observed thatin the notation used for the signals X,Y, and b the value of Z is equalto z^(q).

The operation of the sample rate converter according to the invention isbased on the recognition that if the output signal x_(n) is decimatedafter being filtered by a system filter F_(x) (z) with impulse response{h₀, h₁, . . . , h_(K-1) } the resulting sequence y_(n) can be describedby: ##EQU1## If the sequence x_(n) is known, y_(n) is a q-timesdecimated version of F_(x) (z). X(z) where X(z) is the z-transform ofthe sequence x_(n). In the sample rate converter according to theinvention, the sequence x_(n) has to be determined from y_(n). In orderto do so, (1) can be written as: ##EQU2## From (2) it can be seen that aweighted sum over the sequence {x_(nq-q+1), x_(nq) } can be recursivelydetermined from y_(n) and a weighted sum over the past sequence{x_(nq-K+1), . . . , x_(nq-q) }. In the sample rate converter accordingto FIG. 1, the weighted sum over the past sequence is determined by theweighting summer 4, and the subtraction of the weighted sum over thepast sequence from the input sample y_(n) is performed by thesubtracter 1. The weighted sum over the sequence {x_(nq-q+1), . . . ,x_(nq) } is available as the signal B_(n). The task of the mapper 3 isto provide the q samples of the sequence {x_(nq-q+1), . . . , x_(nq) }in response to the signal B_(n). This however cannot be done in a uniqueway, but there exist a large number of sequences {x_(nq-q+1), . . ,x_(nq) } which have a weighted sum B_(n). The values of x can be foundwith an exhaustive search minimizing the absolute value of the errorbetween B_(n) and the sum over the sequence {x_(nq-q+1), . . . , x_(nq)}. The weighted summer 3 derives a decimated feedback signal from theoutput signal. In order to reduce the amount of aliasing duringdecimation the filter F_(x) (z) should have good suppression outside thefrequency range of the input signal. In addition if spectrum correctionis to be avoided, F_(x) (z) should be substantially constant in thefrequency range of the input signal. A suitable choice for the transferfunction of the filter F_(x) (z) is the transfer function of a combfilter or an approximation thereof. For the transfer function of thefilter F_(x) (z) can be written: ##EQU3## In (3) c is the DC gain of thefilter and m is the order of the filter F_(x) (z). Inducing the property(1-α^(n))=(1-α)·(1+α+α² +. . . α^(n-1)) into (3) results in: ##EQU4##

For m=2, (4) can be expanded into ##EQU5##

If c is chosen such that c/q^(m) is an integer power of 2, the filteraccording to (4) can be very easily be implemented. The weighted summercan be realized in the form of a look up table having stored the samplesh_(q),h_(q+1), . . . ,h_(K-1) of the impulse response of (4). In thiscase the value of K is m·(q-1)-1. The inputs of the look up table areconstituted by the sequence of output samples {x_(nq-K+1), . . . ,X_(nq-q) }.

In the sample rate converter according to FIG. 2, the input is connectedto an input of combiner 17. In the combiner 17, the input signal isapplied to a first input of a subtracter 10. The output of thesubtracter 10 is connected to a first input of a noise shaping filter18. The output of the filter 18, constituting the output of thecombining 17 is connected to an input of the mapping arrangement 21. Inthe mapping arrangement 21 the input signal B is applied to an input ofa mapper 20. The output of the mapper 20 is connected to an input of aparallel to serial converter 22, to an input of a look up table 14 andto the input of a delay element 16. The output of the look up table,carrying the further signal, is connected to a second input of the noiseshaping filter 18. The output of the delay element 16 is connected to aninput of a look up table 12. The output of the look up table 12,carrying the feedback signal is connected to a second input of thesubtracter 10.

The embodiment according to FIG. 2 is based on the requirement to obtainnoise shaping of the quantization error introduced in the mappingprocess. This quantization error can be modelled by an additive noisesource whose output signal is added to the output signal of the mapper.Because the structure of the sample rate converter resembles that of asigma-delta modulator, the noise shaping properties of a sigma-deltamodulator are taken as starting point for the derivation of the requiredchanges of the structure of the sample rate converter according to theinvention to incorporate noise shaping.

For a sigma-delta modulator can be written:

    U(z)=M(z)·Y(z)+G(z)·E(z)                 (6)

In (6) U(z) is the z-transform of the output signal of the sigma-deltamodulator, M(z) is the transfer function for the input signal of thesigma-delta modulator, Y(z) is the z-transform of the input signal, G(z)is the noise transfer function of the sigma-delta modulator, and E(z) isthe z-transform of the quantization error. For the following analysisthe filter function F_(x) (z) is rewritten as: ##EQU6##

If it is assumed that the error signal in the sample rate converteraccording to the invention has to be shaped with a noise transferfunction G(Z) and that the expression for U(Z) of the sample rateconverter according to the invention is similar to that of (6), with zbeing replaced by Z=z^(q) due to the down sampling operation, (2) can bewritten as:

    X.sub.f.sbsb.xi (Z)=M(Z){Y(Z)+G(Z)·E(Z)}-Z.sup.-1 X.sub.f.sbsb.x2 (Z)                                                       (8)

In (8) X_(f).sbsb.xi (Z) is the q-times decimated version of F_(x1) (z)X(z) and X_(fx2) (Z) is the q-times decimated version of F_(x2)(z)·X(z). The signal B(Z) is equal to X_(fx1) (Z)+E(Z). Substituting (8)in the above mentioned expression for B(Z) gives a value of B(Z) equalto: ##EQU7##

The embodiment according to FIG. 2 is arranged for implementing (9). Thecombination of the delay element 16 and the look up table 12 is arrangedfor determining the signal Z⁻¹ X_(fx2) (Z) from the output signal of themapper 20 and the look up table 14 is arranged for determining thesignal X_(fx1) (Z). The filter 18 is arranged for filtering the outputsignal of the subtracter 10 according to the transfer functionM(Z)/G(Z), and for filtering the output signal of the look up table 14by the transfer function {G(Z)-1}/G(Z). The transfer function G can bechosen according to similar stability criteria as used in the design ofloop filters in sigma delta modulators.

In the sample rate converter according to FIG. 3, an input signal isapplied to an input of a sample and hold circuit 24. The output of thesample and hold circuit 34 is connected to a first input of a subtracter26. The output of the adder 26 is connected to a first input of an adder28. The output of the adder 28 is connected to an input of a subtracter30 and to an input of a delay element 38. The output of the delayelement 38 is connected to a second input of the adder 28.

The output of the subtracter 30 is connected to a first input of anadder 32. The output of the adder 32 is connected to an input of amapper 34 and to an input of a delay element 44. The output of the delayelement 44 is connected to a second input of the subtracter 32.

The output of the mapper 34 is connected to an input of a parallel toseries converter 36 and to the input of a delay element 46. The outputof the delay element 46 is connected to an input of a look up table 40and to an input of a look up table 42. The output of the look up table40, with output signal X_(f3), is connected to a second input of thesubtracter 26. The output of the look up table 42 is connected to asecond input of the subtracter 30.

The sample rate converter according to FIG. 3 is obtained by choosingG(Z) to be equal to (1-Z⁻¹)², and M(Z) being equal to 1. Substitutingthese value in (9) results in: ##EQU8## X_(fx1) +X_(fx2) can be replacedby X_(fx3), with X_(fx3) being equal to: ##EQU9##

In the block diagram according to FIG. 3, the signal Z⁻¹ X_(fx3) (Z) isgenerated by the combination of the delay unit 46 and the look up table40. The signal Z⁻¹ X_(fx1),(Z) is generated by the combination of thedelay unit 46 and the look up table 42. The transfer functions 1/(1-Z⁻¹)and 1/(1-Z₋₁)² are realized by a cascade connection of two integrators,the first integrator comprising the adder 28 and the delay element 38,and the second integrator comprising the adder 32 and the delay element46.

If H(z) is chosen to be a second order comb filter having an impulseresponse defined by (5), f_(x3) (k) can be written as: ##EQU10##

Consequently, X_(fx3) can be generated by using only a few exclusive ORgates for adding the samples x_(nq-i).

In the sample rate converter according to FIG. 4, the input signal isapplied to an input of a sample and hold circuit 24. The output of thesample and hold circuit 24 is connected to a first input of a subtracter26. The output of the subtracter 26 is connected to a first input of anadder 43. The output of the adder 43 is connected to an input of a delayelement 45, an input of an adder 47 and to the input of a multiplier 54.The output of the delay element 45 is connected to a second input of theadder 43.

The output of the adder 47 is connected to an input of a delay element48, an input of an adder 50 and to the input of a multiplier 56. Theoutput of the delay element 48 is connected to a second input of theadder 47.

The output of the adder 50 is connected to an input of a delay element52, and to an input of a multiplier 58. The output of the delay element52 is connected to a second input of the adder 50.

The output of the multiplier 54 is connected to a first input of anadder 60. The output of the multiplier 56 is connected to a second inputof the adder 60. The output of the multiplier 58 is connected to a thirdinput of the adder 60.

The output of the adder 60 is connected to an input of a mapper 62. Theoutput of the mapper 62 is connected to an input of a parallel to seriesconverter 64 and to an input of a delay element 66. The output of thedelay element 66 is connected to an input of a look up table 41. Theoutput of the look up table 41 is connected to a second input of thesubtracter 26.

The sample rate converter according to FIG. 4 is obtained by choosingM(Z) to be equal to 1-G(Z). The function G(Z) is chosen to be equal to:##EQU11## C being a constant. Substituting these values in (9) resultsin: ##EQU12## In which the term {1-G(Z)}/G(Z)} can be written as:##EQU13##

The look up table 41 in the converter according to FIG. 4 is arrangedfor generating the signal X_(fx2) (Z)+Z⁻¹ X_(fx1) (Z).

The values chosen for a,b and c are 2.5, 1.5, and 0.75 respectively.

The input of the mapper 34 according to FIG. 5 is connected to an inputof a quantizer 70. The output of the quantiser, carrying an outputsignal representing the quantization level, is connected to an input ofa ROM 72. At the output of the ROM 72 the output of the mapper isavailable. It is observed that the look up tables in the feed back pathcan be incorporated in the ROM 72. In that case the mapper 34 generatesmore than one output signal.

As was explained earlier, the task of the mapper 34 is to derive from aninput signal B_(n) a sequence of q samples x_(nq-q+1). . . x_(nq)according to the equation ##EQU14##

If the number of possible values of x is limited to p, the number ofvalues of B_(n) which exactly are equal to (18) cannot exceed q^(P). Away of implementing the mapper is to quantize the signal B_(n) and use aROM for generating the sequence X_(nq-q+1). . . x_(nq) in response tothe quantised version of B_(n).

An improved mapping algorithm includes filtering of the quantizationerror in such a way that the error signal does not have descretefrequency components in the frequency band of the input signal. Thefilter F_(x1) (z) is a filter with impulse response h₀,h₁, . . . ,h_(q-2),h_(q-1), with h₀ ≠0. A vector x is defined as {x₀,x₁, . .,x_(q-1) } and the vector Y is defined as {Y₀,Y₁, . . Y_(q-1) } Theimpulse response of the F_(x1) (z) can be cast in a q×q lower triangularToeplitz matrix:

The relation between x and y can be described as H·x_(T) =Y^(T). It isobserved that B_(n) is equal to H_(q) ·X^(T) +ε_(q), in which H_(q) isthe last row of the matrix H, and ε_(q) is the quantization errorinvolved with B_(n). The vector Y can now be expressed as: ##EQU15##Y=Y+ε={y₀ +ε₀,y₁ +ε₁, . . . , Y_(q-2) +ε_(q-2),B_(n) +ε_(q-1) }, inwhich y₀,y₁, . . . ,Y_(q-2) are still unknown, and ε_(i) is thequantization error in the samples y_(i). By stating initially h_(q-1)·x₀ =B, and x₁. . . x_(q-1) =0, for the vector Y can now be found:##EQU16## (20) is derived using H ·x^(T) =Y^(T), with neglecting theerrors ε. When the errors ε^(i) are known, the value of x can becalculated according to:

    x.sup.T =H.sup.-1 (Y.sup.T +ε.sup.T)               (19)

    x.sup.T =H.sup.-1 (Y.sup.T +ε.sup.T)

(22) has to be calculated recursively using starting values x₀ and ε₀.Due to the fact that H is a lower triangular Toeplitz matrix, itsinverse has a special structure where all its diagonal elements areequal to 1/h₀, and all elements above the diagonal are zero. Theelements h_(i),j of H⁻¹ can generally be described as h_(q),q-i+j, whereh_(q),k is the k^(th) element in the q^(th) row of H⁻¹. These relationscan be used in a recursive procedure to find the values of x^(i) fromthe value of B as is given below. ##EQU17## In (23) Q[z] is aquantization operation which quantizes the value z to one of the allowedquantization values. (23) can be calculated by a mapper using aprocessor, or using a quantizer followed by a table. The quantizerlevels of the quantizer can be determined beforehand by performing (23)for all possible values of B. The quantization levels for the quantizerare those values at which the sequence X_(nq-q+1). . . x_(nq) changes.

I claim:
 1. A signal converter for converting an input signal having afirst sampling rate into an output signal having a second sampling ratelarger than the first sampling rate, said signal converter comprisingcombining means for deriving a combined signal from the input signal anda feedback signal, and mapping means for deriving from a sample of thecombined signal a sequence of samples of the output signal, the mappingmeans being further arranged for deriving the feedback signal fromsamples of the combined signal, wherein the combining means are arrangedfor deriving one single combined signal, and the mapping means arearranged such that the derived feedback signal represents a decimatedand anti alias filtered version of the output signal.
 2. The signalconverter according to claim 1, wherein the mapping means comprisedecimating means for deriving the feedback signal by decimating a signalrepresenting the output signal.
 3. The signal converter according toclaim 1, wherein the combining means comprise a noise shaping filter forobtaining the combined signal.
 4. The signal converter according toclaim 3, wherein the mapping means are arranged for providing a furthersignal representing a downsampled version of the output signal, and thenoise shaping filter also is arranged for deriving a filtered furthersignal for obtaining the combined signal.
 5. The signal converteraccording to claim 1, wherein in deriving the feedback signal themapping means have an impulse response corresponding at least partly tothe impulse response of a comb filter.
 6. The signal converter accordingto claim 5, wherein the mapping means are arranged for filtering theerror signal according to a high-pass transfer function.
 7. The signalconverter according to claim 1, wherein the mapping means are arrangedfor recursively determining the samples of the output signal from afiltered error signal, the error signal being representative of thedifference between the input sample and a weighted sum of output samplesalready determined.